The Use of Bernard Walther's Astronomical Observations: Theory and Observation in Early Modern Astronomy

See Aaboe A. and de Solla Price D. J. , “Qualitative measurement in Antiquity: The derivation of accurate parameters from crude but crucial observations”, in Mélanges Alexandre Koyré (Paris, 1964), i, 1–20; Goldstein B. R. , “Theory and observation in medieval astronomy”, Isis, lxiii (1972), 39–47; Hartner W. , “The role of observations in ancient and medieval astronomy”, Journal for the history of astronomy, viii (1977), 1–11; Goldstein B. R. , “Medieval observations of solar and lunar eclipses”, Archives internationales d'histoire des sciences, xxix (1979), 101–56.

Kepler J. , Gesammelte Werke (Munich, 1937–), iii, 178. See also Gingerich O. , “Kepler's treatment of redundant observations, or the computer versus Kepler revisited”, in Internationales Kepler-Symposium, Weil der Stadt, 1971 (Hildesheim, 1973), 307–14. For Galileo's interesting discussion of redundant, inconsistent observations, see Dialogue concerning the two chief world systems, the opening arguments of the third day.

See Kremer R. L. , “Bernard Walther's astronomical observations”, Journal for the history of astronomy, xi (1980), 174–91.

See Petz H. , “Urkundliche Nachrichten über den literarischen Nachlass Regiomontanus und B. Walters 1478–1522”, Mitteilungen des Vereins für Geschichte der Stadt Nürnberg, vii (1888), 247–62; Zinner E. , Leben und Wirken des Johannes Müller von Königsberg, genannt Regiomontanus, 2d ed. (Osnabruck, 1968), 245–65, 293–371; Pilz K. , “Bernhard Walther und seine astronomischen Beobachtungsstände”, Mitteilungen des Vereins für Geschichte der Stadt Nürnberg, lvii (1970), 184–6; Pilz K. , 600 Jahre Astronomie in Nürnberg (Nuremberg, 1977), 97–100.

Schöner J. (ed.), Scripta clarissimi mathematici M. Ioannis Regiomontani (Nuremberg, 1544); republished in facsimile in Regiomontanus J. , Opera collectanea, ed. by Schmeidler F. (Osnabruck, 1972), 567–752.

Snel W. , Coeli et siderum in eo errantium Hassiacae (Leiden, 1618); Barrettus L. [ Curtz A. ], Historia coelestis (Augsburg, 1666); Riccioli G. B. , Astronomiae reformatae (Bologna, 1665), vol. ii.

Questions such as how Copernicus learned of Walther's observations before their publication, why in De revolutionibus, V, 30, he mistakenly attributed two of the observations to Schöner though in the autograph copy he initially wrote that Walther had taken all three of the measurements, or whether Copernicus might have had access to more of Walther's data all raise intriguing historical issues that cannot be discussed here. See Copernicus N. Complete works, ii: On the revolutions, translated with commentary by Rosen E. (Warsaw, 1978), 433–4.

For studies of Copernicus's Mercury model, see Gingerich O. , “The Mercury model from Antiquity to Kepler”, Actes du XII^e Congrès international d'Histoire des Sciences, 1968, iiia (Paris, 1971), 57–64; Hartner W. , “Ptolemy, Azarquiel, Ibn Al-Shātir, and Copernicus on Mercury: A study of parameters”, Archives internationales d'histoire des sciences, xxiv (1974), 2–25, 367–9; Swerdlow N. W. , “Copernicus's four models of Mercury”, Colloquia Copernicana, iii (Studia Copernicana, xiii) (Wroclaw, 1975), 141–55.

In his Mysterium cosmographicum, Kepler accused Copernicus of altering observations to simplify computations. See Kepler , Gesammelte Werke (ref. 2), i, 59–65. For specific examples of this, see the discussion following Dobrzycki J. , “The role of observations in the work of Copernicus”, in Beer A. and Strand K. A. (eds), Copernicus yesterday and today (Vistas in astronomy, xvii) (Oxford, 1975), 33–35; Swerdlow N. M. , “The holograph of De revolutionibus and the chronology of its composition”, Journal for the history of astronomy, v (1974), 195–8; Swerdlow N. M. , “On Copernicus' theory of precession”, in Westman R. S. Jr (ed.), The Copernican achievement (Berkeley, 1975), 49–98. For an opposite view, see Bialas V. , “Die Planetenbeobachtungen des Copernicus—zur Genauigkeit der Beobachtungen und ihrer Funktion in seinem Weltsystem”, Philosophia naturalis, xiv (1973), 328–52.

I have derived the values of Table 1 from Copernicus N. , De revolutionibus orbium coelestium libri sex (Nuremberg, 1543), ff. 169r–v; Copernicus N. , Complete works, i: The manuscript of Nicholas Copernicus' ‘On the revolutions’ facsimile (London, 1972), ff. 180v–181r; Copernicus , Complete works , ii (ref. 7), 285, 433–4; Copernicus N. , Gesamtausgabe, ii: De revolutionibus orbium caelestium, Testkritisches Ausgabe, ed. by Zeller F. and Zeller C. (Munich, 1949), 347–9; Copernicus N. , Opera omnia, ii: De revolutionibus libri sex, ed. by Gansiniec R. (Warsaw, 1975), 294–6. The critical editions do not always agree on the emendations herein discussed.

Each of the critical editions gives 26° as the initial value for the third observation. Rosen in Copernicus, Complete works , ii (ref. 7), 434, claimed that Copernicus “inadvertently” omitted the fraction. Yet a closer examination of the autograph, guided by a knowledge of Copernicus's intentions, indicates that on f. 181r, line 9, Copernicus first wrote “xxvi s” before scratching out the “s” and adding the revised fraction in the margin.

Copernicus wrote 163°30′ as the final value in the autograph, and this value appeared in the 1543 edition. Yet in stating Mercury's elongation and in the subsequent calculations, he rounded the value of the longitude to 163°32′.

Here Copernicus changed the longitude in the autograph to 26°55′ (cum deunce unius gradus), but the 1543 edition listed it as 26°6′ (cum decima unius gradus). In computing Mercury's elongation, Copernicus used 26°56′ as the planet's longitude.

On f. 181r, lines 17, 19–20 of the autograph, Copernicus did change the value for Mercury's anomaly of parallax over both time periods between the three observations. Yet both these changes were > 1°, and undoubtedly were made to correct computational errors, as Rosen suggested in Copernicus, Complete works, ii (ref. 7), 434. Copernicus did not change the recorded times of observation.

Given λ₁ = 163°32′, he calculated angle EGF to be 49°8' for the first figure of V, 30, when for his λ₁, the value should in fact be 46°42′. Copernicus committed a less serious error in computing the geometry of the initial situation at t₁ finding for the same figure side EF = 10,371 parts, and angle CEF = 2°30′, when the respective values should be 10,459 parts and 2°32′. As the iterated calculations using different values for λ₁ would not require recomputing side EF and angle CEF, I have assumed that Copernicus carried these errors through all his computations, and have carried them through mine as well. At most, however, these errors shift values buried in the calculations only about 2′, and affect the final predicted longitudes (λ₂, λ₃) not at all, quite unlike the major error in finding angle EGF which did shift the computed λ₂ slightly.

In addition, positions for Mercury computed from Copernicus's completed prosthaphaereses tables for Walther's observational times match the altered positions better than Walther's original longitudes. Copernicus thus helped himself twice as he juggled Walther's data. See Gingerich O. , “Early Copernican ephemerides”, in Science and history: Studies in honor of Edward Rosen (Studia Copernicana, xvi) (Wroclaw, 1978), 410. Zinner E. , Entstehung und Ausbreitung der Coppernicanischen Lehre (Erlangen, 1943), 213–14, also noticed that Copernicus's longitudes in V, 30 did not match Walther's in the Scripta. He suggested that Copernicus may have carelessly confused two sheets of paper when writing V, 30, one containing Walther's observed positions, the other listing values calculated for Walther's observational times from Copernicus's model. My re-creation of Copernicus's computational procedures, based on changes in the autograph, casts doubt on Zinner's explanation.

Rheticus G. J. , Ephemerides novae seu expositio positus diurni siderum (Leipzig, 1550), sig. A3v. It is possible that Rheticus did not remember correctly the substance of this conversation. For example, he has Copernicus complaining about the lack of modern observations of Mercury, and thus exhorting Rheticus to begin observing himself. Yet by the summer of 1539 when Rheticus arrived in Frauenberg, Copernicus must have had Walther's data and must have completed V, 30, for that chapter is written on papers D and E which Copernicus used only through the late 1530s. See Swerdlow , “The holograph” (ref. 9), 190–4, and Zinner , Entstehung und Ausbreitung (ref. 16), 241–2.

Copernicus markedly overestimated both the precision of his models and his own observational skills. See Gingerich , “Early Copernican ephemerides” (ref. 16), 403–11. Yet his estimation of the precision of his observations was quite close to the precision of Walther's armillary measurements (slightly under 10′). See Kremer , “Walther's observations” (ref. 3).

For his recomputation of De revolutionibus, V, 30, see Reinhold E. , “Commentarius in opus revolutionum Copernici”, MS. fol. lat. 391, ff. 280v–88r, Deutsche Staatsbibliothek, Berlin. Prof. Gingerich provided me with a microfilm copy of this manuscript.

Mästlin's copy of the Scripta, recently identified as such by Gingerich O. , “Science in the Age of Copernicus”, Harvard Library bulletin, xxvi (1978), 403, is in Houghton Library, Harvard University, GC.R2636.544s (A).

One of Mästlin's annotated copies of the 1543 edition of De revolutionibus is in the Stadtbibliothek, Schaffhausen, Switzerland. The other, recently identified by Prof. Gingerich , is in the Württembergische Landesbibliothek, Stuttgart. I have consulted Prof. Gingerich's microfilms of these books. Mästlin corrected V, 30 in the Schaffhausen copy slightly more thoroughly than in the Stuttgart copy, but both display identically the emendations mentioned here. See ff. 169r-v of both copies, and ff. 55r (misnumbered 59), 58r, 60r of Mästlin's Scripta.

See Grafton A. , “Michael Maestlin's account of Copernican planetary theory”, Proceedings of the American Philosophical Society, xcvii (1973), 523–50.

Kepler , Gesammelte Werke (ref. 2), xiii, 77–79; Grafton , op. cit. (ref. 22), 531. Mästlin's letter, in somewhat revised form, appeared in the Mysterium cosmographicum. See Kepler , Gesammelte Werke (ref. 2), i, 67–68.

In his Epitome astronomiae (Heidelberg, 1582), 484, Mästlin presented a longitude of Spica measured by Walther.

“Inquisitio elevationis polaris quae est Norimbergae ex altitudinibus solis a Johanne de Monte Regio et eius discipulo Bernardo Walthero”, Col. Vindob. Pal. 10686.1, ff. 58r–60r, Österreichische Nationalbibliothek, Vienna. The Hill Monastic Manuscripts Library, St John's University, sent me a copy of this manuscript. Since Tycho did not correct the altitudes for refraction, the MS. probably pre-dates 1588. See Maeyama Y. , “The historical development of solar theories in the late-sixteenth and seventeenth centuries”, in Vistas in astronomy, xvi (1974), 35–60.

See Brahe T. , Opera omnia, ed. by Dreyer J. L. E. (Copenhagen, 1913–29), ii, 38–45. For later works setting parameters with Walther's altitudes, see Wendelin G. , Loxais seu de obliquitate solis diatriba (Antwerp, 1627), 3, 26; Riccioli G. B. , Almagestum novum astronomiam veterem novamque complectens (Bologna, 1651), i, 156156, 371–2; Wurzelbauer J. P. , Uranies Noricae basis astronomico-geographica (Nuremberg, 1697), 36–43; Flamsteed J. , Historia coelestis Britannica (London, 1725), iii, 34–38; Cassini J. , Éléments d'astronomie (Paris, 1740), passim; de Lacaille N. L. , “Sur les élémens de la théorie du soleil”, Histoire de l'Académie royale (1749), i, 219–24; Mayer J. T. , “Latitudo geographica urbis Norimbergae”, Commentarii societatis regiae scientiarum Gottingensis, i (1752), 373–8.

Brahe , Opera omnia (ref. 26), ii, 59–62.

Kepler , Gesammelte Werke (ref. 2), xiv, 130, 208, 300; ii, 137–42; xviii, 174, 198.

Kepler , Gesammelte Werke (ref. 2), xviii, 237. Kepler's analysis, entitled “Consideratio observationum Regiomontani et Waltheri”, was intended as an appendix to the Tabulae, but remained unpublished until included in Kepler J. , Opera omnia, ed. by Frisch C. (Frankfurt-Erlangen, 1858–71), vi, 723–74. For the kudos offered Walther , see vi, 752, 769.

Kepler , Gesammelte Werke (ref. 2), xviii, 174; Kepler , Opera omnia (ref. 29), vi, 730–4, 751–6, 762–3; Bialas V. , Die Rudolphinischen Tafeln von Johannes Kepler: Mathematische und astronomische Grundlagen (Abhandlungen der Bayerische Akademie der Wissenschaften, Math.-Naturwiss. Klasse, n.f. cxxxix) (Munich, 1969), 112–14, 125.

Kepler , Opera omnia (ref. 29), vi, 730–1; Kepler , Gesammelte Werke (ref. 2), x, 39, 44.

I thank Prof. Owen Gingerich for criticizing earlier drafts of this article, and Shank Michael for helping me translate some of Kepler's Latin prose.